62,247 research outputs found
On the Inefficiency of the Uniform Price Auction
We present our results on Uniform Price Auctions, one of the standard
sealed-bid multi-unit auction formats, for selling multiple identical units of
a single good to multi-demand bidders. Contrary to the truthful and
economically efficient multi-unit Vickrey auction, the Uniform Price Auction
encourages strategic bidding and is socially inefficient in general. The
uniform pricing rule is, however, widely popular by its appeal to the natural
anticipation, that identical items should be identically priced. In this work
we study equilibria of the Uniform Price Auction for bidders with (symmetric)
submodular valuation functions, over the number of units that they win. We
investigate pure Nash equilibria of the auction in undominated strategies; we
produce a characterization of these equilibria that allows us to prove that a
fraction 1-1/e of the optimum social welfare is always recovered in undominated
pure Nash equilibrium -- and this bound is essentially tight. Subsequently, we
study the auction under the incomplete information setting and prove a bound of
4-2/k on the economic inefficiency of (mixed) Bayes Nash equilibria that are
supported by undominated strategies.Comment: Additions and Improvements upon SAGT 2012 results (and minor
corrections on the previous version
Pricing Multi-Unit Markets
We study the power and limitations of posted prices in multi-unit markets,
where agents arrive sequentially in an arbitrary order. We prove upper and
lower bounds on the largest fraction of the optimal social welfare that can be
guaranteed with posted prices, under a range of assumptions about the
designer's information and agents' valuations. Our results provide insights
about the relative power of uniform and non-uniform prices, the relative
difficulty of different valuation classes, and the implications of different
informational assumptions. Among other results, we prove constant-factor
guarantees for agents with (symmetric) subadditive valuations, even in an
incomplete-information setting and with uniform prices
A Branch-and-Price Algorithm for Bin Packing Problem
Bin Packing Problem examines the minimum number of identical bins needed to pack a set of items of various sizes. Employing branch-and-bound and column generation usually requires designation of the problem-specific branching rules compatible with the nature of the pricing sub-problem of column generation, or alternatively it requires determination of the k-best solutions of knapsack problem at level kth of the tree. Instead, we present a new approach to deal with the pricing sub-problem of column generation which handles two-dimensional knapsack problems. Furthermore, a set of new upper bounds for Bin Packing Problem is introduced in this work which employs solutions of the continuous relaxation of the set-covering formulation of Bin Packing Problem. These high quality upper bounds are computed inexpensively and dominate the ones generated by state-of-the-art methods
The Pricing War Continues: On Competitive Multi-Item Pricing
We study a game with \emph{strategic} vendors who own multiple items and a
single buyer with a submodular valuation function. The goal of the vendors is
to maximize their revenue via pricing of the items, given that the buyer will
buy the set of items that maximizes his net payoff.
We show this game may not always have a pure Nash equilibrium, in contrast to
previous results for the special case where each vendor owns a single item. We
do so by relating our game to an intermediate, discrete game in which the
vendors only choose the available items, and their prices are set exogenously
afterwards.
We further make use of the intermediate game to provide tight bounds on the
price of anarchy for the subset games that have pure Nash equilibria; we find
that the optimal PoA reached in the previous special cases does not hold, but
only a logarithmic one.
Finally, we show that for a special case of submodular functions, efficient
pure Nash equilibria always exist
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